SAN DIEGO -- It's been a bumpy road for the Los Angeles Dodgers since they returned stateside after beginning the season with two wins against Arizona in Australia.

Reigning NL Cy Young Award winner Clayton Kershaw is expected to miss the bulk of April with a swollen muscle in his left upper back, and now reliever Brian Wilson will be placed on the disabled list with what manager Don Mattingly said is nerve irritation in his right elbow.

Mattingly said Wilson had an MRI on Monday that showed nerve irritation. Mattingly said there was no sign of ligament damage. Wilson had reconstructive surgery in April 2012.

"The MRI overall was not good news, but it was better than it could have been," Mattingly said. "I was pleased and relieved that it wasn't something bigger than what it is. We feel like it's something that just needs to calm down and then kind of built going the other direction."

The Dodgers' bullpen has had a rough go since returning from Sydney. Wilson allowed three runs in the eighth inning of Sunday night's 3-1 loss, and Jansen had to dance out of trouble in the ninth on Tuesday.

"We've had one bad inning, really. We're getting it done, but it's just a little rough right now," he said. "It's not as smooth as it can be. Confident with our guys I think as we get into the normal work, normal days, we'll be OK."

Carl Crawford started the game with a base hit and Puig then drove a 2-1 pitch from Ian Kennedy into the balcony on the third deck of the Western Metal Supply Co. Building in the left-field corner. It was his first homer.

"At the time, when it happens so fast, I don't know if I caught too much plate," Kennedy said. "He did a really good job of getting his hands up. He's a really good hitter. Puig did a good job of hitting what I thought was a good pitch. But he's one of the best hitters in the National League."

It was the second time Kennedy faced the Dodgers since June 11, when, while with Arizona, he hit Puig and Greinke with pitches, inciting a brawl at Dodger Stadium. Kennedy was suspended 10 games. He was traded to the Padres on July 31.

Greinke retired his first 10 batters before Seth Smith homered into a party deck atop the right-field wall, trimming San Diego's deficit to 3-1. Smith earned the start in left field against the right-handed Greinke after homering to start an eighth-inning rally in a 3-1 win Sunday night.

Greinke (1-0) went five innings, allowing two runs and two hits while striking out five and walking two.

The Dodgers took a 3-0 lead in the fourth when Dee Gordon singled in Juan Uribe. Uribe doubled to right-center with two outs and took third on second baseman Jedd Gyorko's error.

Gyorko had gone into the shallow outfield to take the throw from right fielder Chris Denorfia. He turned and started to throw, but apparently realized there was no play at third and tried to hold up, losing his grip on the ball. That allowed Uribe to advance.

San Diego pulled to 3-2 in the fifth when Gyorko drew a leadoff walk and eventually scored on wild pitch.

Kennedy (0-1) allowed three runs and five hits in five innings.

Greinke was making his third start in San Diego since the Dodgers and Padres brawled here on April 11. That melee started after Greinke hit Carlos Quentin with a pitch. Quentin rushed the mound and slammed into Greinke, whose left collarbone was broken. Quentin started this season on the disabled list with a bone bruise in his left knee.

Game notes
Kershaw won't be ready to come off the disabled list when he's eligible to be activated on April 14. The Dodgers said Kershaw will slowly work his way back for the next two to three weeks. He will then be re-evaluated to determine when he can start throwing at increased velocity. Kershaw will likely have to make a rehab start before he can return, Mattingly said. ... The series concludes Wednesday night when Dan Haren of the Dodgers and Tyson Ross of the Padres make their 2014 debuts. ... To celebrate the 10th anniversary of Petco Park opening, David Wells (first start), Brian Giles (first hit) and Mark Loretta (first Padres' home run) threw out ceremonial first pitches.